A:AnswerYou can definitely find a nice 1080p 144 to 165 hertz monitor within that price range, and yes it would 100% be possible but just make sure the 3050 can run well with your tv's resolution !
A:AnswerNothing will optimally run Skyrim, special edition or not, because Skyrim isn't optimized to be run on anything. But It will run the game very well and as long as Skyrim's own spaghetti code doesn't get in the way, you shouldn't have any problems.